All Questions
Tagged with prior hierarchical-bayesian
52
questions
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172
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In Bayesian hierarchical models, what is the difference between an Empirical Bayesian approach to parametrising priors vs using flat hyperpriors
Say I have a simple hierarchical model, where:
$y_{g,i} = \beta_g x_{g,i} + e_{g,i}$
where $g$ represents the group, $i$ represents the individual within the group, and $e$ is the error. So the ...
- 71
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1k
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Choosing priors for the parameters of Gamma distribution
Suppose that $X_1, X_2, \cdots, X_n$ is a sample drawn from a Gamma distribution with parameter $\alpha$ and $\beta$. Then, the likelihood function can be written as follows:
\begin{equation}
L(\...
- 153
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220
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Hierachical Bayesian modelling using brms: how to insert a prior that reflects cut-offs of Reaction Times distribution?
I am running a hierarchical Bayesian model using brms on reaction times (RTs) of a GoNogo task. The predictors are categorical and include the 3 stimuli/condition that participants observed and the 2 ...
- 21
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25
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Data-informed grouping of covariates in Bayesian Hierarchical Modeling?
Is there a way to place a prior on the first stage's betas that allows the second stage groups to be determined from the data? I am working with co-exposures where I am not super confident in how they ...
- 13
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70
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Conjugate Hyperpriors
I heard it was possible to have a Bayesian model with likelihood, prior and hyperprior that has a posterior of closed form, by choosing a conjugate prior and conjugate hyperprior. But I struggle to ...
- 31
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436
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Is my Stan model correct? The Jeffreys prior for a heteroscedastic mixed-effects model
I am using rstan to obtain MCMC samples from a heteroscedastic mixed-effects model with different residual variances $\sigma_j^2$ for each experimental condition $j$.
One assumption is the Jeffreys ...
1
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0
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147
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Prior for Variance Covariance Matrix [closed]
Why in Bayesian Hierarchical Modelling the prior corresponding to a Variance Covariance Matrix is taken to be Inverse Wishart Distribution not Wishart Distribution?
- 41
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102
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Showing that a posterior is Normal given improper prior
I am having difficulty showing the following problem and I suspect it has something to do with my lack of understanding of the question. The question is this:
Suppose we have an improper prior ...
- 125
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0
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73
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How to parametrize a posterior to use it as a prior in Bayesian statistics?
In my problem, I have two sets of parameters, $\theta_1$ and $\theta_2$, and two datasets $d_1,d_2$ that constrain them with a known likelihood function. There is a certain 'hierarchy' in the model: ...
- 151
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131
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Behaviour of the marginal in the limit for an infinite sequence of hierarchical priors
Consider the following model:
$$y \sim \text{Exponential}(\lambda_0) \\
\lambda_i | \lambda_{i+1} \sim \text{Exponential}(\lambda_i+1) \\
\text{for } i=1,2,\dots,d\\
\lambda_{d+1} = k
$$
With an ...
- 2,480
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0
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135
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When to stop the chain of priors in Bayesian hierarchical models?
From Wkipedia's article on hyperprior:
In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, on a parameter of a prior distribution.
There will be some ...
- 183
2
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0
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42
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Why do we reparameterize before assigning a hyperprior distribution?
I am studying hierarchical models, and trying to understand a point in the book where they try to decide on a non-informative hyperprior distribution.
The hyperparameters is $\alpha$ and $\beta$ for a ...
- 83
1
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0
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17
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Group level distribution for positive parameters in Bayesian multilevel models
I am doing a lot of modeling with models that require some parameters to be positive by design. However, I am struggling to figure out which approach works best when I try to use multilevel modeling ...
- 2,671
2
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1
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538
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How to choose a non-informative or weakly informative hyper priors for my hierarchical bayesian model?
I am learning Bayes on "Applied Bayesian Statistics" by MK Cowles.
The chapter about "Bayesian Hierarchical Models" mentioned an example that we estimate a softball player’s ...
- 221
1
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1
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278
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For Prior definition in bayesian regression with R package MCMCglmm, how to convey different strength of believe via parameter nu?
I understand the strength of the Prior is set via parameter nu however, I can not find information what nu expresses in statistical terms, e.g. how strong would a prior that is similar to the number ...
